ReasoningAges 13-15

Universal set & Venn complements

Use inclusion-exclusion within a universal set to find how many items belong to neither subset. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 13-15

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 45 students, n(A) = 21, n(B) = 23, and n(A ∩ B) = 10. How many students are in neither A nor B?
45 s · 21 · 23 · 10 · Universal set & Venn compl…
2. In a group of 23 students, n(A) = 13, n(B) = 13, and n(A ∩ B) = 9. How many students are in neither A nor B?
23 s · 13 · 13 · 9 · Universal set & Venn compl…
3. In a group of 41 students, n(A) = 24, n(B) = 23, and n(A ∩ B) = 9. How many students are in neither A nor B?
41 s · 24 · 23 · 9 · Universal set & Venn compl…
4. In a group of 37 students, n(A) = 17, n(B) = 16, and n(A ∩ B) = 5. How many students are in neither A nor B?
37 s · 17 · 16 · 5 · Universal set & Venn compl…
5. In a group of 54 students, n(A) = 22, n(B) = 22, and n(A ∩ B) = 3. How many students are in neither A nor B?
54 s · 22 · 22 · 3 · Universal set & Venn compl…
6. In a group of 32 students, n(A) = 7, n(B) = 14, and n(A ∩ B) = 3. How many students are in neither A nor B?
32 s · 7 · 14 · 3 · Universal set & Venn compl…
7. In a group of 48 students, n(A) = 16, n(B) = 30, and n(A ∩ B) = 10. How many students are in neither A nor B?
48 s · 16 · 30 · 10 · Universal set & Venn compl…
8. In a group of 41 students, n(A) = 27, n(B) = 19, and n(A ∩ B) = 11. How many students are in neither A nor B?
41 s · 27 · 19 · 11 · Universal set & Venn compl…
9. In a group of 20 students, n(A) = 8, n(B) = 8, and n(A ∩ B) = 4. How many students are in neither A nor B?
20 s · 8 · 8 · 4 · Universal set & Venn compl…
10. In a group of 41 students, n(A) = 15, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
41 s · 15 · 19 · 2 · Universal set & Venn compl…
11. In a group of 59 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 8. How many students are in neither A nor B?
59 s · 27 · 27 · 8 · Universal set & Venn compl…
12. In a group of 53 students, n(A) = 23, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
53 s · 23 · 26 · 6 · Universal set & Venn compl…

12 questions · Seed 52 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 13-15

Universal set & Venn complements

Answers and reasoning. Review before teaching.

1. In a group of 45 students, n(A) = 21, n(B) = 23, and n(A ∩ B) = 10. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 21 + 23 − 10 = 34, leaving 45 − 34 = 11 in neither set.
2. In a group of 23 students, n(A) = 13, n(B) = 13, and n(A ∩ B) = 9. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 13 + 13 − 9 = 17, leaving 23 − 17 = 6 in neither set.
3. In a group of 41 students, n(A) = 24, n(B) = 23, and n(A ∩ B) = 9. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 24 + 23 − 9 = 38, leaving 41 − 38 = 3 in neither set.
4. In a group of 37 students, n(A) = 17, n(B) = 16, and n(A ∩ B) = 5. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 17 + 16 − 5 = 28, leaving 37 − 28 = 9 in neither set.
5. In a group of 54 students, n(A) = 22, n(B) = 22, and n(A ∩ B) = 3. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 22 + 22 − 3 = 41, leaving 54 − 41 = 13 in neither set.
6. In a group of 32 students, n(A) = 7, n(B) = 14, and n(A ∩ B) = 3. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 7 + 14 − 3 = 18, leaving 32 − 18 = 14 in neither set.
7. In a group of 48 students, n(A) = 16, n(B) = 30, and n(A ∩ B) = 10. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 16 + 30 − 10 = 36, leaving 48 − 36 = 12 in neither set.
8. In a group of 41 students, n(A) = 27, n(B) = 19, and n(A ∩ B) = 11. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 27 + 19 − 11 = 35, leaving 41 − 35 = 6 in neither set.
9. In a group of 20 students, n(A) = 8, n(B) = 8, and n(A ∩ B) = 4. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 8 + 8 − 4 = 12, leaving 20 − 12 = 8 in neither set.
10. In a group of 41 students, n(A) = 15, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 15 + 19 − 2 = 32, leaving 41 − 32 = 9 in neither set.
11. In a group of 59 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 8. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 27 + 27 − 8 = 46, leaving 59 − 46 = 13 in neither set.
12. In a group of 53 students, n(A) = 23, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 23 + 26 − 6 = 43, leaving 53 − 43 = 10 in neither set.

12 questions · Seed 52 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 13-15

Universal set & Venn complements

Take your time. Show your thinking.

1. In a group of 45 students, n(A) = 21, n(B) = 23, and n(A ∩ B) = 10. How many students are in neither A nor B?
45 s · 21 · 23 · 10 · Universal set & Venn compl…
2. In a group of 23 students, n(A) = 13, n(B) = 13, and n(A ∩ B) = 9. How many students are in neither A nor B?
23 s · 13 · 13 · 9 · Universal set & Venn compl…
3. In a group of 41 students, n(A) = 24, n(B) = 23, and n(A ∩ B) = 9. How many students are in neither A nor B?
41 s · 24 · 23 · 9 · Universal set & Venn compl…
4. In a group of 37 students, n(A) = 17, n(B) = 16, and n(A ∩ B) = 5. How many students are in neither A nor B?
37 s · 17 · 16 · 5 · Universal set & Venn compl…
5. In a group of 54 students, n(A) = 22, n(B) = 22, and n(A ∩ B) = 3. How many students are in neither A nor B?
54 s · 22 · 22 · 3 · Universal set & Venn compl…
6. In a group of 32 students, n(A) = 7, n(B) = 14, and n(A ∩ B) = 3. How many students are in neither A nor B?
32 s · 7 · 14 · 3 · Universal set & Venn compl…
7. In a group of 48 students, n(A) = 16, n(B) = 30, and n(A ∩ B) = 10. How many students are in neither A nor B?
48 s · 16 · 30 · 10 · Universal set & Venn compl…
8. In a group of 41 students, n(A) = 27, n(B) = 19, and n(A ∩ B) = 11. How many students are in neither A nor B?
41 s · 27 · 19 · 11 · Universal set & Venn compl…
9. In a group of 20 students, n(A) = 8, n(B) = 8, and n(A ∩ B) = 4. How many students are in neither A nor B?
20 s · 8 · 8 · 4 · Universal set & Venn compl…
10. In a group of 41 students, n(A) = 15, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
41 s · 15 · 19 · 2 · Universal set & Venn compl…
11. In a group of 59 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 8. How many students are in neither A nor B?
59 s · 27 · 27 · 8 · Universal set & Venn compl…
12. In a group of 53 students, n(A) = 23, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
53 s · 23 · 26 · 6 · Universal set & Venn compl…

12 questions · Seed 52 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 13-15

Universal set & Venn complements

Answers and reasoning. Review before teaching.

1. In a group of 45 students, n(A) = 21, n(B) = 23, and n(A ∩ B) = 10. How many students are in neither A nor B?
11
By inclusion-exclusion, n(A ∪ B) = 21 + 23 − 10 = 34, leaving 45 − 34 = 11 in neither set.
2. In a group of 23 students, n(A) = 13, n(B) = 13, and n(A ∩ B) = 9. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 13 + 13 − 9 = 17, leaving 23 − 17 = 6 in neither set.
3. In a group of 41 students, n(A) = 24, n(B) = 23, and n(A ∩ B) = 9. How many students are in neither A nor B?
3
By inclusion-exclusion, n(A ∪ B) = 24 + 23 − 9 = 38, leaving 41 − 38 = 3 in neither set.
4. In a group of 37 students, n(A) = 17, n(B) = 16, and n(A ∩ B) = 5. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 17 + 16 − 5 = 28, leaving 37 − 28 = 9 in neither set.
5. In a group of 54 students, n(A) = 22, n(B) = 22, and n(A ∩ B) = 3. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 22 + 22 − 3 = 41, leaving 54 − 41 = 13 in neither set.
6. In a group of 32 students, n(A) = 7, n(B) = 14, and n(A ∩ B) = 3. How many students are in neither A nor B?
14
By inclusion-exclusion, n(A ∪ B) = 7 + 14 − 3 = 18, leaving 32 − 18 = 14 in neither set.
7. In a group of 48 students, n(A) = 16, n(B) = 30, and n(A ∩ B) = 10. How many students are in neither A nor B?
12
By inclusion-exclusion, n(A ∪ B) = 16 + 30 − 10 = 36, leaving 48 − 36 = 12 in neither set.
8. In a group of 41 students, n(A) = 27, n(B) = 19, and n(A ∩ B) = 11. How many students are in neither A nor B?
6
By inclusion-exclusion, n(A ∪ B) = 27 + 19 − 11 = 35, leaving 41 − 35 = 6 in neither set.
9. In a group of 20 students, n(A) = 8, n(B) = 8, and n(A ∩ B) = 4. How many students are in neither A nor B?
8
By inclusion-exclusion, n(A ∪ B) = 8 + 8 − 4 = 12, leaving 20 − 12 = 8 in neither set.
10. In a group of 41 students, n(A) = 15, n(B) = 19, and n(A ∩ B) = 2. How many students are in neither A nor B?
9
By inclusion-exclusion, n(A ∪ B) = 15 + 19 − 2 = 32, leaving 41 − 32 = 9 in neither set.
11. In a group of 59 students, n(A) = 27, n(B) = 27, and n(A ∩ B) = 8. How many students are in neither A nor B?
13
By inclusion-exclusion, n(A ∪ B) = 27 + 27 − 8 = 46, leaving 59 − 46 = 13 in neither set.
12. In a group of 53 students, n(A) = 23, n(B) = 26, and n(A ∩ B) = 6. How many students are in neither A nor B?
10
By inclusion-exclusion, n(A ∪ B) = 23 + 26 − 6 = 43, leaving 53 − 43 = 10 in neither set.

12 questions · Seed 52 · Age guidance, not curriculum certification